/*
    Tables for Marching Cubes
    http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
*/

// edge table maps 8-bit flag representing which cube vertices are inside
// the isosurface to 12-bit number indicating which edges are intersected
uint edgeTable[256] = {
	0x0  , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
	0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
	0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
	0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
	0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
	0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
	0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
	0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
	0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
	0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
	0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
	0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
	0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
	0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
	0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
	0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
	0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
	0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
	0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
	0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
	0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
	0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
	0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
	0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
	0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
	0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
	0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
	0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
	0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
	0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
	0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
	0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0
};

// triangle table maps same cube vertex index to a list of up to 5 triangles
// which are built from the interpolated edge vertices
#define X 255
#ifndef XYZ_DIR_EDGE
#define XYZ_DIR_EDGE	1
#endif
#if XYZ_DIR_EDGE
uint triTable[256][16] = {
	{X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 4, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 6, 10, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{6, 8, 4, 10, 8, 6, X, X, X, X, X, X, X, X, X, X},
	{6, 2, 11, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 4, 6, 2, 11, X, X, X, X, X, X, X, X, X, X},
	{10, 2, 11, 0, 2, 10, X, X, X, X, X, X, X, X, X, X},
	{2, 8, 4, 2, 11, 8, 11, 10, 8, X, X, X, X, X, X, X},
	{4, 9, 2, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 9, 2, 8, 9, 0, X, X, X, X, X, X, X, X, X, X},
	{6, 10, 0, 2, 4, 9, X, X, X, X, X, X, X, X, X, X},
	{6, 9, 2, 6, 10, 9, 10, 8, 9, X, X, X, X, X, X, X},
	{4, 11, 6, 9, 11, 4, X, X, X, X, X, X, X, X, X, X},
	{0, 11, 6, 0, 8, 11, 8, 9, 11, X, X, X, X, X, X, X},
	{4, 10, 0, 4, 9, 10, 9, 11, 10, X, X, X, X, X, X, X},
	{10, 8, 11, 11, 8, 9, X, X, X, X, X, X, X, X, X, X},
	{1, 5, 8, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{1, 4, 0, 5, 4, 1, X, X, X, X, X, X, X, X, X, X},
	{0, 6, 10, 8, 1, 5, X, X, X, X, X, X, X, X, X, X},
	{1, 6, 10, 1, 5, 6, 5, 4, 6, X, X, X, X, X, X, X},
	{6, 2, 11, 8, 1, 5, X, X, X, X, X, X, X, X, X, X},
	{4, 1, 5, 4, 0, 1, 6, 2, 11, X, X, X, X, X, X, X},
	{10, 2, 11, 10, 0, 2, 8, 1, 5, X, X, X, X, X, X, X},
	{2, 11, 10, 2, 10, 5, 2, 5, 4, 5, 10, 1, X, X, X, X},
	{8, 1, 5, 4, 9, 2, X, X, X, X, X, X, X, X, X, X},
	{9, 1, 5, 9, 2, 1, 2, 0, 1, X, X, X, X, X, X, X},
	{10, 0, 6, 8, 1, 5, 2, 4, 9, X, X, X, X, X, X, X},
	{1, 5, 9, 10, 1, 9, 10, 9, 2, 10, 2, 6, X, X, X, X},
	{4, 11, 6, 4, 9, 11, 5, 8, 1, X, X, X, X, X, X, X},
	{6, 9, 11, 6, 1, 9, 6, 0, 1, 5, 9, 1, X, X, X, X},
	{1, 5, 8, 10, 0, 9, 10, 9, 11, 9, 0, 4, X, X, X, X},
	{1, 5, 9, 1, 9, 10, 10, 9, 11, X, X, X, X, X, X, X},
	{10, 7, 1, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{10, 7, 1, 0, 8, 4, X, X, X, X, X, X, X, X, X, X},
	{0, 7, 1, 6, 7, 0, X, X, X, X, X, X, X, X, X, X},
	{8, 7, 1, 8, 4, 7, 4, 6, 7, X, X, X, X, X, X, X},
	{6, 2, 11, 10, 7, 1, X, X, X, X, X, X, X, X, X, X},
	{4, 0, 8, 6, 2, 11, 1, 10, 7, X, X, X, X, X, X, X},
	{7, 2, 11, 7, 1, 2, 1, 0, 2, X, X, X, X, X, X, X},
	{2, 11, 7, 4, 2, 7, 4, 7, 1, 4, 1, 8, X, X, X, X},
	{10, 7, 1, 2, 4, 9, X, X, X, X, X, X, X, X, X, X},
	{0, 9, 2, 0, 8, 9, 1, 10, 7, X, X, X, X, X, X, X},
	{0, 7, 1, 0, 6, 7, 2, 4, 9, X, X, X, X, X, X, X},
	{2, 6, 7, 2, 7, 8, 2, 8, 9, 1, 8, 7, X, X, X, X},
	{11, 4, 9, 11, 6, 4, 10, 7, 1, X, X, X, X, X, X, X},
	{1, 10, 7, 0, 8, 6, 8, 11, 6, 8, 9, 11, X, X, X, X},
	{7, 1, 0, 7, 0, 9, 7, 9, 11, 9, 0, 4, X, X, X, X},
	{7, 1, 8, 7, 8, 11, 11, 8, 9, X, X, X, X, X, X, X},
	{10, 5, 8, 7, 5, 10, X, X, X, X, X, X, X, X, X, X},
	{10, 4, 0, 10, 7, 4, 7, 5, 4, X, X, X, X, X, X, X},
	{0, 5, 8, 0, 6, 5, 6, 7, 5, X, X, X, X, X, X, X},
	{6, 7, 4, 4, 7, 5, X, X, X, X, X, X, X, X, X, X},
	{10, 5, 8, 10, 7, 5, 11, 6, 2, X, X, X, X, X, X, X},
	{11, 6, 2, 10, 7, 0, 7, 4, 0, 7, 5, 4, X, X, X, X},
	{8, 0, 2, 8, 2, 7, 8, 7, 5, 11, 7, 2, X, X, X, X},
	{2, 11, 7, 2, 7, 4, 4, 7, 5, X, X, X, X, X, X, X},
	{5, 10, 7, 5, 8, 10, 4, 9, 2, X, X, X, X, X, X, X},
	{10, 7, 5, 10, 5, 2, 10, 2, 0, 2, 5, 9, X, X, X, X},
	{2, 4, 9, 0, 6, 8, 6, 5, 8, 6, 7, 5, X, X, X, X},
	{9, 2, 6, 9, 6, 5, 5, 6, 7, X, X, X, X, X, X, X},
	{10, 7, 8, 8, 7, 5, 11, 6, 4, 11, 4, 9, X, X, X, X},
	{7, 5, 0, 7, 0, 10, 5, 9, 0, 6, 0, 11, 9, 11, 0, X},
	{9, 11, 0, 9, 0, 4, 11, 7, 0, 8, 0, 5, 7, 5, 0, X},
	{9, 11, 7, 5, 9, 7, X, X, X, X, X, X, X, X, X, X},
	{11, 3, 7, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 4, 7, 11, 3, X, X, X, X, X, X, X, X, X, X},
	{10, 0, 6, 7, 11, 3, X, X, X, X, X, X, X, X, X, X},
	{6, 8, 4, 6, 10, 8, 7, 11, 3, X, X, X, X, X, X, X},
	{6, 3, 7, 2, 3, 6, X, X, X, X, X, X, X, X, X, X},
	{6, 3, 7, 6, 2, 3, 4, 0, 8, X, X, X, X, X, X, X},
	{10, 3, 7, 10, 0, 3, 0, 2, 3, X, X, X, X, X, X, X},
	{7, 10, 8, 7, 8, 2, 7, 2, 3, 4, 2, 8, X, X, X, X},
	{2, 4, 9, 11, 3, 7, X, X, X, X, X, X, X, X, X, X},
	{9, 0, 8, 9, 2, 0, 11, 3, 7, X, X, X, X, X, X, X},
	{0, 6, 10, 2, 4, 9, 7, 11, 3, X, X, X, X, X, X, X},
	{7, 11, 3, 6, 10, 2, 10, 9, 2, 10, 8, 9, X, X, X, X},
	{3, 4, 9, 3, 7, 4, 7, 6, 4, X, X, X, X, X, X, X},
	{0, 8, 9, 0, 9, 7, 0, 7, 6, 7, 9, 3, X, X, X, X},
	{4, 9, 3, 0, 4, 3, 0, 3, 7, 0, 7, 10, X, X, X, X},
	{3, 7, 10, 3, 10, 9, 9, 10, 8, X, X, X, X, X, X, X},
	{7, 11, 3, 1, 5, 8, X, X, X, X, X, X, X, X, X, X},
	{1, 4, 0, 1, 5, 4, 3, 7, 11, X, X, X, X, X, X, X},
	{6, 10, 0, 7, 11, 3, 8, 1, 5, X, X, X, X, X, X, X},
	{11, 3, 7, 6, 10, 5, 6, 5, 4, 5, 10, 1, X, X, X, X},
	{3, 6, 2, 3, 7, 6, 1, 5, 8, X, X, X, X, X, X, X},
	{6, 2, 7, 7, 2, 3, 4, 0, 1, 4, 1, 5, X, X, X, X},
	{8, 1, 5, 10, 0, 7, 0, 3, 7, 0, 2, 3, X, X, X, X},
	{5, 4, 10, 5, 10, 1, 4, 2, 10, 7, 10, 3, 2, 3, 10, X},
	{4, 9, 2, 5, 8, 1, 11, 3, 7, X, X, X, X, X, X, X},
	{7, 11, 3, 1, 5, 2, 1, 2, 0, 2, 5, 9, X, X, X, X},
	{0, 6, 10, 1, 5, 8, 2, 4, 9, 7, 11, 3, X, X, X, X},
	{10, 2, 6, 10, 9, 2, 10, 1, 9, 5, 9, 1, 7, 11, 3, X},
	{8, 1, 5, 4, 9, 7, 4, 7, 6, 7, 9, 3, X, X, X, X},
	{7, 6, 9, 7, 9, 3, 6, 0, 9, 5, 9, 1, 0, 1, 9, X},
	{0, 7, 10, 0, 3, 7, 0, 4, 3, 9, 3, 4, 8, 1, 5, X},
	{3, 7, 10, 3, 10, 9, 1, 5, 10, 5, 9, 10, X, X, X, X},
	{11, 1, 10, 3, 1, 11, X, X, X, X, X, X, X, X, X, X},
	{1, 11, 3, 1, 10, 11, 0, 8, 4, X, X, X, X, X, X, X},
	{11, 0, 6, 11, 3, 0, 3, 1, 0, X, X, X, X, X, X, X},
	{8, 4, 6, 8, 6, 3, 8, 3, 1, 3, 6, 11, X, X, X, X},
	{6, 1, 10, 6, 2, 1, 2, 3, 1, X, X, X, X, X, X, X},
	{4, 0, 8, 6, 2, 10, 2, 1, 10, 2, 3, 1, X, X, X, X},
	{0, 2, 1, 1, 2, 3, X, X, X, X, X, X, X, X, X, X},
	{8, 4, 2, 8, 2, 1, 1, 2, 3, X, X, X, X, X, X, X},
	{11, 1, 10, 11, 3, 1, 9, 2, 4, X, X, X, X, X, X, X},
	{0, 8, 2, 2, 8, 9, 1, 10, 11, 1, 11, 3, X, X, X, X},
	{4, 9, 2, 0, 6, 3, 0, 3, 1, 3, 6, 11, X, X, X, X},
	{3, 1, 6, 3, 6, 11, 1, 8, 6, 2, 6, 9, 8, 9, 6, X},
	{10, 3, 1, 10, 4, 3, 10, 6, 4, 9, 3, 4, X, X, X, X},
	{8, 9, 6, 8, 6, 0, 9, 3, 6, 10, 6, 1, 3, 1, 6, X},
	{4, 9, 3, 4, 3, 0, 0, 3, 1, X, X, X, X, X, X, X},
	{3, 1, 8, 9, 3, 8, X, X, X, X, X, X, X, X, X, X},
	{5, 11, 3, 5, 8, 11, 8, 10, 11, X, X, X, X, X, X, X},
	{0, 5, 4, 0, 11, 5, 0, 10, 11, 3, 5, 11, X, X, X, X},
	{11, 3, 5, 6, 11, 5, 6, 5, 8, 6, 8, 0, X, X, X, X},
	{11, 3, 5, 11, 5, 6, 6, 5, 4, X, X, X, X, X, X, X},
	{6, 2, 3, 6, 3, 8, 6, 8, 10, 8, 3, 5, X, X, X, X},
	{2, 3, 10, 2, 10, 6, 3, 5, 10, 0, 10, 4, 5, 4, 10, X},
	{5, 8, 0, 5, 0, 3, 3, 0, 2, X, X, X, X, X, X, X},
	{5, 4, 2, 3, 5, 2, X, X, X, X, X, X, X, X, X, X},
	{2, 4, 9, 11, 3, 8, 11, 8, 10, 8, 3, 5, X, X, X, X},
	{2, 0, 5, 2, 5, 9, 0, 10, 5, 3, 5, 11, 10, 11, 5, X},
	{6, 8, 0, 6, 5, 8, 6, 11, 5, 3, 5, 11, 2, 4, 9, X},
	{9, 2, 6, 9, 6, 5, 11, 3, 6, 3, 5, 6, X, X, X, X},
	{8, 10, 3, 8, 3, 5, 10, 6, 3, 9, 3, 4, 6, 4, 3, X},
	{0, 10, 6, 9, 3, 5, X, X, X, X, X, X, X, X, X, X},
	{5, 8, 0, 5, 0, 3, 4, 9, 0, 9, 3, 0, X, X, X, X},
	{5, 9, 3, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{5, 3, 9, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{4, 0, 8, 9, 5, 3, X, X, X, X, X, X, X, X, X, X},
	{0, 6, 10, 9, 5, 3, X, X, X, X, X, X, X, X, X, X},
	{8, 6, 10, 8, 4, 6, 9, 5, 3, X, X, X, X, X, X, X},
	{11, 6, 2, 3, 9, 5, X, X, X, X, X, X, X, X, X, X},
	{6, 2, 11, 4, 0, 8, 3, 9, 5, X, X, X, X, X, X, X},
	{2, 10, 0, 2, 11, 10, 3, 9, 5, X, X, X, X, X, X, X},
	{3, 9, 5, 2, 11, 4, 11, 8, 4, 11, 10, 8, X, X, X, X},
	{5, 2, 4, 3, 2, 5, X, X, X, X, X, X, X, X, X, X},
	{5, 0, 8, 5, 3, 0, 3, 2, 0, X, X, X, X, X, X, X},
	{2, 5, 3, 2, 4, 5, 0, 6, 10, X, X, X, X, X, X, X},
	{6, 3, 2, 6, 8, 3, 6, 10, 8, 8, 5, 3, X, X, X, X},
	{11, 5, 3, 11, 6, 5, 6, 4, 5, X, X, X, X, X, X, X},
	{11, 5, 3, 6, 5, 11, 6, 8, 5, 6, 0, 8, X, X, X, X},
	{0, 4, 5, 0, 5, 11, 0, 11, 10, 3, 11, 5, X, X, X, X},
	{5, 3, 11, 5, 11, 8, 8, 11, 10, X, X, X, X, X, X, X},
	{3, 8, 1, 9, 8, 3, X, X, X, X, X, X, X, X, X, X},
	{4, 3, 9, 4, 0, 3, 0, 1, 3, X, X, X, X, X, X, X},
	{8, 3, 9, 8, 1, 3, 10, 0, 6, X, X, X, X, X, X, X},
	{10, 1, 3, 10, 3, 4, 10, 4, 6, 9, 4, 3, X, X, X, X},
	{3, 8, 1, 3, 9, 8, 2, 11, 6, X, X, X, X, X, X, X},
	{6, 2, 11, 4, 0, 9, 0, 3, 9, 0, 1, 3, X, X, X, X},
	{1, 9, 8, 1, 3, 9, 0, 2, 10, 2, 11, 10, X, X, X, X},
	{11, 10, 4, 11, 4, 2, 10, 1, 4, 9, 4, 3, 1, 3, 4, X},
	{8, 2, 4, 8, 1, 2, 1, 3, 2, X, X, X, X, X, X, X},
	{0, 1, 2, 1, 3, 2, X, X, X, X, X, X, X, X, X, X},
	{6, 10, 0, 2, 4, 1, 2, 1, 3, 1, 4, 8, X, X, X, X},
	{6, 10, 1, 6, 1, 2, 2, 1, 3, X, X, X, X, X, X, X},
	{8, 6, 4, 8, 3, 6, 8, 1, 3, 3, 11, 6, X, X, X, X},
	{11, 6, 0, 11, 0, 3, 3, 0, 1, X, X, X, X, X, X, X},
	{1, 3, 4, 1, 4, 8, 3, 11, 4, 0, 4, 10, 11, 10, 4, X},
	{11, 10, 1, 3, 11, 1, X, X, X, X, X, X, X, X, X, X},
	{1, 10, 7, 5, 3, 9, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 4, 1, 10, 7, 9, 5, 3, X, X, X, X, X, X, X},
	{7, 0, 6, 7, 1, 0, 5, 3, 9, X, X, X, X, X, X, X},
	{9, 5, 3, 8, 4, 1, 4, 7, 1, 4, 6, 7, X, X, X, X},
	{10, 7, 1, 11, 6, 2, 5, 3, 9, X, X, X, X, X, X, X},
	{3, 9, 5, 6, 2, 11, 0, 8, 4, 1, 10, 7, X, X, X, X},
	{5, 3, 9, 7, 1, 11, 1, 2, 11, 1, 0, 2, X, X, X, X},
	{4, 1, 8, 4, 7, 1, 4, 2, 7, 11, 7, 2, 9, 5, 3, X},
	{5, 2, 4, 5, 3, 2, 7, 1, 10, X, X, X, X, X, X, X},
	{10, 7, 1, 0, 8, 3, 0, 3, 2, 3, 8, 5, X, X, X, X},
	{4, 3, 2, 4, 5, 3, 6, 7, 0, 7, 1, 0, X, X, X, X},
	{3, 2, 8, 3, 8, 5, 2, 6, 8, 1, 8, 7, 6, 7, 8, X},
	{10, 7, 1, 11, 6, 3, 6, 5, 3, 6, 4, 5, X, X, X, X},
	{6, 3, 11, 6, 5, 3, 6, 0, 5, 8, 5, 0, 10, 7, 1, X},
	{1, 0, 11, 1, 11, 7, 0, 4, 11, 3, 11, 5, 4, 5, 11, X},
	{5, 3, 11, 5, 11, 8, 7, 1, 11, 1, 8, 11, X, X, X, X},
	{3, 10, 7, 3, 9, 10, 9, 8, 10, X, X, X, X, X, X, X},
	{4, 3, 9, 0, 3, 4, 0, 7, 3, 0, 10, 7, X, X, X, X},
	{0, 9, 8, 0, 7, 9, 0, 6, 7, 7, 3, 9, X, X, X, X},
	{3, 9, 4, 3, 4, 7, 7, 4, 6, X, X, X, X, X, X, X},
	{6, 2, 11, 10, 7, 9, 10, 9, 8, 9, 7, 3, X, X, X, X},
	{0, 9, 4, 0, 3, 9, 0, 10, 3, 7, 3, 10, 6, 2, 11, X},
	{9, 8, 7, 9, 7, 3, 8, 0, 7, 11, 7, 2, 0, 2, 7, X},
	{3, 9, 4, 3, 4, 7, 2, 11, 4, 11, 7, 4, X, X, X, X},
	{7, 8, 10, 7, 2, 8, 7, 3, 2, 4, 8, 2, X, X, X, X},
	{10, 7, 3, 10, 3, 0, 0, 3, 2, X, X, X, X, X, X, X},
	{6, 7, 8, 6, 8, 0, 7, 3, 8, 4, 8, 2, 3, 2, 8, X},
	{6, 7, 3, 2, 6, 3, X, X, X, X, X, X, X, X, X, X},
	{6, 4, 3, 6, 3, 11, 4, 8, 3, 7, 3, 10, 8, 10, 3, X},
	{11, 6, 0, 11, 0, 3, 10, 7, 0, 7, 3, 0, X, X, X, X},
	{0, 4, 8, 7, 3, 11, X, X, X, X, X, X, X, X, X, X},
	{11, 7, 3, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{9, 7, 11, 5, 7, 9, X, X, X, X, X, X, X, X, X, X},
	{9, 7, 11, 9, 5, 7, 8, 4, 0, X, X, X, X, X, X, X},
	{7, 9, 5, 7, 11, 9, 6, 10, 0, X, X, X, X, X, X, X},
	{11, 5, 7, 11, 9, 5, 10, 8, 6, 8, 4, 6, X, X, X, X},
	{9, 6, 2, 9, 5, 6, 5, 7, 6, X, X, X, X, X, X, X},
	{0, 8, 4, 6, 2, 5, 6, 5, 7, 5, 2, 9, X, X, X, X},
	{10, 5, 7, 10, 2, 5, 10, 0, 2, 2, 9, 5, X, X, X, X},
	{5, 7, 2, 5, 2, 9, 7, 10, 2, 4, 2, 8, 10, 8, 2, X},
	{2, 7, 11, 2, 4, 7, 4, 5, 7, X, X, X, X, X, X, X},
	{8, 2, 0, 8, 7, 2, 8, 5, 7, 11, 2, 7, X, X, X, X},
	{10, 0, 6, 7, 11, 4, 7, 4, 5, 4, 11, 2, X, X, X, X},
	{10, 8, 2, 10, 2, 6, 8, 5, 2, 11, 2, 7, 5, 7, 2, X},
	{6, 4, 7, 4, 5, 7, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 5, 0, 5, 6, 6, 5, 7, X, X, X, X, X, X, X},
	{10, 0, 4, 10, 4, 7, 7, 4, 5, X, X, X, X, X, X, X},
	{10, 8, 5, 7, 10, 5, X, X, X, X, X, X, X, X, X, X},
	{7, 8, 1, 7, 11, 8, 11, 9, 8, X, X, X, X, X, X, X},
	{7, 0, 1, 7, 9, 0, 7, 11, 9, 9, 4, 0, X, X, X, X},
	{0, 6, 10, 8, 1, 11, 8, 11, 9, 11, 1, 7, X, X, X, X},
	{11, 9, 1, 11, 1, 7, 9, 4, 1, 10, 1, 6, 4, 6, 1, X},
	{2, 7, 6, 2, 8, 7, 2, 9, 8, 1, 7, 8, X, X, X, X},
	{0, 1, 9, 0, 9, 4, 1, 7, 9, 2, 9, 6, 7, 6, 9, X},
	{0, 2, 7, 0, 7, 10, 2, 9, 7, 1, 7, 8, 9, 8, 7, X},
	{10, 1, 7, 2, 9, 4, X, X, X, X, X, X, X, X, X, X},
	{2, 7, 11, 4, 7, 2, 4, 1, 7, 4, 8, 1, X, X, X, X},
	{7, 11, 2, 7, 2, 1, 1, 2, 0, X, X, X, X, X, X, X},
	{4, 11, 2, 4, 7, 11, 4, 8, 7, 1, 7, 8, 0, 6, 10, X},
	{7, 11, 2, 7, 2, 1, 6, 10, 2, 10, 1, 2, X, X, X, X},
	{8, 1, 7, 8, 7, 4, 4, 7, 6, X, X, X, X, X, X, X},
	{0, 1, 7, 6, 0, 7, X, X, X, X, X, X, X, X, X, X},
	{8, 1, 7, 8, 7, 4, 10, 0, 7, 0, 4, 7, X, X, X, X},
	{10, 1, 7, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{1, 9, 5, 1, 10, 9, 10, 11, 9, X, X, X, X, X, X, X},
	{0, 8, 4, 1, 10, 5, 10, 9, 5, 10, 11, 9, X, X, X, X},
	{6, 11, 9, 6, 9, 1, 6, 1, 0, 5, 1, 9, X, X, X, X},
	{4, 6, 1, 4, 1, 8, 6, 11, 1, 5, 1, 9, 11, 9, 1, X},
	{1, 9, 5, 10, 9, 1, 10, 2, 9, 10, 6, 2, X, X, X, X},
	{10, 5, 1, 10, 9, 5, 10, 6, 9, 2, 9, 6, 0, 8, 4, X},
	{9, 5, 1, 9, 1, 2, 2, 1, 0, X, X, X, X, X, X, X},
	{9, 5, 1, 9, 1, 2, 8, 4, 1, 4, 2, 1, X, X, X, X},
	{2, 10, 11, 2, 5, 10, 2, 4, 5, 5, 1, 10, X, X, X, X},
	{10, 11, 5, 10, 5, 1, 11, 2, 5, 8, 5, 0, 2, 0, 5, X},
	{4, 5, 11, 4, 11, 2, 5, 1, 11, 6, 11, 0, 1, 0, 11, X},
	{6, 11, 2, 8, 5, 1, X, X, X, X, X, X, X, X, X, X},
	{1, 10, 6, 1, 6, 5, 5, 6, 4, X, X, X, X, X, X, X},
	{1, 10, 6, 1, 6, 5, 0, 8, 6, 8, 5, 6, X, X, X, X},
	{1, 0, 4, 5, 1, 4, X, X, X, X, X, X, X, X, X, X},
	{1, 8, 5, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{10, 11, 8, 11, 9, 8, X, X, X, X, X, X, X, X, X, X},
	{4, 0, 10, 4, 10, 9, 9, 10, 11, X, X, X, X, X, X, X},
	{0, 6, 11, 0, 11, 8, 8, 11, 9, X, X, X, X, X, X, X},
	{4, 6, 11, 9, 4, 11, X, X, X, X, X, X, X, X, X, X},
	{6, 2, 9, 6, 9, 10, 10, 9, 8, X, X, X, X, X, X, X},
	{4, 0, 10, 4, 10, 9, 6, 2, 10, 2, 9, 10, X, X, X, X},
	{0, 2, 9, 8, 0, 9, X, X, X, X, X, X, X, X, X, X},
	{4, 2, 9, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{2, 4, 8, 2, 8, 11, 11, 8, 10, X, X, X, X, X, X, X},
	{10, 11, 2, 0, 10, 2, X, X, X, X, X, X, X, X, X, X},
	{2, 4, 8, 2, 8, 11, 0, 6, 8, 6, 11, 8, X, X, X, X},
	{6, 11, 2, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{6, 4, 8, 10, 6, 8, X, X, X, X, X, X, X, X, X, X},
	{0, 10, 6, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 4, 8, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X}
	};
#else
uint triTable[256][16] = {
	{X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 3, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 1, 9, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{1, 8, 3, 9, 8, 1, X, X, X, X, X, X, X, X, X, X},
	{1, 2, 10, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 3, 1, 2, 10, X, X, X, X, X, X, X, X, X, X},
	{9, 2, 10, 0, 2, 9, X, X, X, X, X, X, X, X, X, X},
	{2, 8, 3, 2, 10, 8, 10, 9, 8, X, X, X, X, X, X, X},
	{3, 11, 2, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 11, 2, 8, 11, 0, X, X, X, X, X, X, X, X, X, X},
	{1, 9, 0, 2, 3, 11, X, X, X, X, X, X, X, X, X, X},
	{1, 11, 2, 1, 9, 11, 9, 8, 11, X, X, X, X, X, X, X},
	{3, 10, 1, 11, 10, 3, X, X, X, X, X, X, X, X, X, X},
	{0, 10, 1, 0, 8, 10, 8, 11, 10, X, X, X, X, X, X, X},
	{3, 9, 0, 3, 11, 9, 11, 10, 9, X, X, X, X, X, X, X},
	{9, 8, 10, 10, 8, 11, X, X, X, X, X, X, X, X, X, X},
	{4, 7, 8, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{4, 3, 0, 7, 3, 4, X, X, X, X, X, X, X, X, X, X},
	{0, 1, 9, 8, 4, 7, X, X, X, X, X, X, X, X, X, X},
	{4, 1, 9, 4, 7, 1, 7, 3, 1, X, X, X, X, X, X, X},
	{1, 2, 10, 8, 4, 7, X, X, X, X, X, X, X, X, X, X},
	{3, 4, 7, 3, 0, 4, 1, 2, 10, X, X, X, X, X, X, X},
	{9, 2, 10, 9, 0, 2, 8, 4, 7, X, X, X, X, X, X, X},
	{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, X, X, X, X},
	{8, 4, 7, 3, 11, 2, X, X, X, X, X, X, X, X, X, X},
	{11, 4, 7, 11, 2, 4, 2, 0, 4, X, X, X, X, X, X, X},
	{9, 0, 1, 8, 4, 7, 2, 3, 11, X, X, X, X, X, X, X},
	{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, X, X, X, X},
	{3, 10, 1, 3, 11, 10, 7, 8, 4, X, X, X, X, X, X, X},
	{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, X, X, X, X},
	{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, X, X, X, X},
	{4, 7, 11, 4, 11, 9, 9, 11, 10, X, X, X, X, X, X, X},
	{9, 5, 4, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{9, 5, 4, 0, 8, 3, X, X, X, X, X, X, X, X, X, X},
	{0, 5, 4, 1, 5, 0, X, X, X, X, X, X, X, X, X, X},
	{8, 5, 4, 8, 3, 5, 3, 1, 5, X, X, X, X, X, X, X},
	{1, 2, 10, 9, 5, 4, X, X, X, X, X, X, X, X, X, X},
	{3, 0, 8, 1, 2, 10, 4, 9, 5, X, X, X, X, X, X, X},
	{5, 2, 10, 5, 4, 2, 4, 0, 2, X, X, X, X, X, X, X},
	{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, X, X, X, X},
	{9, 5, 4, 2, 3, 11, X, X, X, X, X, X, X, X, X, X},
	{0, 11, 2, 0, 8, 11, 4, 9, 5, X, X, X, X, X, X, X},
	{0, 5, 4, 0, 1, 5, 2, 3, 11, X, X, X, X, X, X, X},
	{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, X, X, X, X},
	{10, 3, 11, 10, 1, 3, 9, 5, 4, X, X, X, X, X, X, X},
	{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, X, X, X, X},
	{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, X, X, X, X},
	{5, 4, 8, 5, 8, 10, 10, 8, 11, X, X, X, X, X, X, X},
	{9, 7, 8, 5, 7, 9, X, X, X, X, X, X, X, X, X, X},
	{9, 3, 0, 9, 5, 3, 5, 7, 3, X, X, X, X, X, X, X},
	{0, 7, 8, 0, 1, 7, 1, 5, 7, X, X, X, X, X, X, X},
	{1, 5, 3, 3, 5, 7, X, X, X, X, X, X, X, X, X, X},
	{9, 7, 8, 9, 5, 7, 10, 1, 2, X, X, X, X, X, X, X},
	{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, X, X, X, X},
	{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, X, X, X, X},
	{2, 10, 5, 2, 5, 3, 3, 5, 7, X, X, X, X, X, X, X},
	{7, 9, 5, 7, 8, 9, 3, 11, 2, X, X, X, X, X, X, X},
	{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, X, X, X, X},
	{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, X, X, X, X},
	{11, 2, 1, 11, 1, 7, 7, 1, 5, X, X, X, X, X, X, X},
	{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, X, X, X, X},
	{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, X},
	{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, X},
	{11, 10, 5, 7, 11, 5, X, X, X, X, X, X, X, X, X, X},
	{10, 6, 5, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 3, 5, 10, 6, X, X, X, X, X, X, X, X, X, X},
	{9, 0, 1, 5, 10, 6, X, X, X, X, X, X, X, X, X, X},
	{1, 8, 3, 1, 9, 8, 5, 10, 6, X, X, X, X, X, X, X},
	{1, 6, 5, 2, 6, 1, X, X, X, X, X, X, X, X, X, X},
	{1, 6, 5, 1, 2, 6, 3, 0, 8, X, X, X, X, X, X, X},
	{9, 6, 5, 9, 0, 6, 0, 2, 6, X, X, X, X, X, X, X},
	{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, X, X, X, X},
	{2, 3, 11, 10, 6, 5, X, X, X, X, X, X, X, X, X, X},
	{11, 0, 8, 11, 2, 0, 10, 6, 5, X, X, X, X, X, X, X},
	{0, 1, 9, 2, 3, 11, 5, 10, 6, X, X, X, X, X, X, X},
	{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, X, X, X, X},
	{6, 3, 11, 6, 5, 3, 5, 1, 3, X, X, X, X, X, X, X},
	{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, X, X, X, X},
	{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, X, X, X, X},
	{6, 5, 9, 6, 9, 11, 11, 9, 8, X, X, X, X, X, X, X},
	{5, 10, 6, 4, 7, 8, X, X, X, X, X, X, X, X, X, X},
	{4, 3, 0, 4, 7, 3, 6, 5, 10, X, X, X, X, X, X, X},
	{1, 9, 0, 5, 10, 6, 8, 4, 7, X, X, X, X, X, X, X},
	{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, X, X, X, X},
	{6, 1, 2, 6, 5, 1, 4, 7, 8, X, X, X, X, X, X, X},
	{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, X, X, X, X},
	{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, X, X, X, X},
	{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, X},
	{3, 11, 2, 7, 8, 4, 10, 6, 5, X, X, X, X, X, X, X},
	{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, X, X, X, X},
	{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, X, X, X, X},
	{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, X},
	{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, X, X, X, X},
	{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, X},
	{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, X},
	{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, X, X, X, X},
	{10, 4, 9, 6, 4, 10, X, X, X, X, X, X, X, X, X, X},
	{4, 10, 6, 4, 9, 10, 0, 8, 3, X, X, X, X, X, X, X},
	{10, 0, 1, 10, 6, 0, 6, 4, 0, X, X, X, X, X, X, X},
	{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, X, X, X, X},
	{1, 4, 9, 1, 2, 4, 2, 6, 4, X, X, X, X, X, X, X},
	{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, X, X, X, X},
	{0, 2, 4, 4, 2, 6, X, X, X, X, X, X, X, X, X, X},
	{8, 3, 2, 8, 2, 4, 4, 2, 6, X, X, X, X, X, X, X},
	{10, 4, 9, 10, 6, 4, 11, 2, 3, X, X, X, X, X, X, X},
	{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, X, X, X, X},
	{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, X, X, X, X},
	{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, X},
	{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, X, X, X, X},
	{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, X},
	{3, 11, 6, 3, 6, 0, 0, 6, 4, X, X, X, X, X, X, X},
	{6, 4, 8, 11, 6, 8, X, X, X, X, X, X, X, X, X, X},
	{7, 10, 6, 7, 8, 10, 8, 9, 10, X, X, X, X, X, X, X},
	{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, X, X, X, X},
	{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, X, X, X, X},
	{10, 6, 7, 10, 7, 1, 1, 7, 3, X, X, X, X, X, X, X},
	{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, X, X, X, X},
	{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, X},
	{7, 8, 0, 7, 0, 6, 6, 0, 2, X, X, X, X, X, X, X},
	{7, 3, 2, 6, 7, 2, X, X, X, X, X, X, X, X, X, X},
	{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, X, X, X, X},
	{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, X},
	{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, X},
	{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, X, X, X, X},
	{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, X},
	{0, 9, 1, 11, 6, 7, X, X, X, X, X, X, X, X, X, X},
	{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, X, X, X, X},
	{7, 11, 6, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{7, 6, 11, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{3, 0, 8, 11, 7, 6, X, X, X, X, X, X, X, X, X, X},
	{0, 1, 9, 11, 7, 6, X, X, X, X, X, X, X, X, X, X},
	{8, 1, 9, 8, 3, 1, 11, 7, 6, X, X, X, X, X, X, X},
	{10, 1, 2, 6, 11, 7, X, X, X, X, X, X, X, X, X, X},
	{1, 2, 10, 3, 0, 8, 6, 11, 7, X, X, X, X, X, X, X},
	{2, 9, 0, 2, 10, 9, 6, 11, 7, X, X, X, X, X, X, X},
	{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, X, X, X, X},
	{7, 2, 3, 6, 2, 7, X, X, X, X, X, X, X, X, X, X},
	{7, 0, 8, 7, 6, 0, 6, 2, 0, X, X, X, X, X, X, X},
	{2, 7, 6, 2, 3, 7, 0, 1, 9, X, X, X, X, X, X, X},
	{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, X, X, X, X},
	{10, 7, 6, 10, 1, 7, 1, 3, 7, X, X, X, X, X, X, X},
	{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, X, X, X, X},
	{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, X, X, X, X},
	{7, 6, 10, 7, 10, 8, 8, 10, 9, X, X, X, X, X, X, X},
	{6, 8, 4, 11, 8, 6, X, X, X, X, X, X, X, X, X, X},
	{3, 6, 11, 3, 0, 6, 0, 4, 6, X, X, X, X, X, X, X},
	{8, 6, 11, 8, 4, 6, 9, 0, 1, X, X, X, X, X, X, X},
	{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, X, X, X, X},
	{6, 8, 4, 6, 11, 8, 2, 10, 1, X, X, X, X, X, X, X},
	{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, X, X, X, X},
	{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, X, X, X, X},
	{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, X},
	{8, 2, 3, 8, 4, 2, 4, 6, 2, X, X, X, X, X, X, X},
	{0, 4, 2, 4, 6, 2, X, X, X, X, X, X, X, X, X, X},
	{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, X, X, X, X},
	{1, 9, 4, 1, 4, 2, 2, 4, 6, X, X, X, X, X, X, X},
	{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, X, X, X, X},
	{10, 1, 0, 10, 0, 6, 6, 0, 4, X, X, X, X, X, X, X},
	{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, X},
	{10, 9, 4, 6, 10, 4, X, X, X, X, X, X, X, X, X, X},
	{4, 9, 5, 7, 6, 11, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 3, 4, 9, 5, 11, 7, 6, X, X, X, X, X, X, X},
	{5, 0, 1, 5, 4, 0, 7, 6, 11, X, X, X, X, X, X, X},
	{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, X, X, X, X},
	{9, 5, 4, 10, 1, 2, 7, 6, 11, X, X, X, X, X, X, X},
	{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, X, X, X, X},
	{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, X, X, X, X},
	{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, X},
	{7, 2, 3, 7, 6, 2, 5, 4, 9, X, X, X, X, X, X, X},
	{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, X, X, X, X},
	{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, X, X, X, X},
	{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, X},
	{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, X, X, X, X},
	{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, X},
	{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, X},
	{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, X, X, X, X},
	{6, 9, 5, 6, 11, 9, 11, 8, 9, X, X, X, X, X, X, X},
	{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, X, X, X, X},
	{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, X, X, X, X},
	{6, 11, 3, 6, 3, 5, 5, 3, 1, X, X, X, X, X, X, X},
	{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, X, X, X, X},
	{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, X},
	{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, X},
	{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, X, X, X, X},
	{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, X, X, X, X},
	{9, 5, 6, 9, 6, 0, 0, 6, 2, X, X, X, X, X, X, X},
	{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, X},
	{1, 5, 6, 2, 1, 6, X, X, X, X, X, X, X, X, X, X},
	{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, X},
	{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, X, X, X, X},
	{0, 3, 8, 5, 6, 10, X, X, X, X, X, X, X, X, X, X},
	{10, 5, 6, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{11, 5, 10, 7, 5, 11, X, X, X, X, X, X, X, X, X, X},
	{11, 5, 10, 11, 7, 5, 8, 3, 0, X, X, X, X, X, X, X},
	{5, 11, 7, 5, 10, 11, 1, 9, 0, X, X, X, X, X, X, X},
	{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, X, X, X, X},
	{11, 1, 2, 11, 7, 1, 7, 5, 1, X, X, X, X, X, X, X},
	{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, X, X, X, X},
	{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, X, X, X, X},
	{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, X},
	{2, 5, 10, 2, 3, 5, 3, 7, 5, X, X, X, X, X, X, X},
	{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, X, X, X, X},
	{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, X, X, X, X},
	{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, X},
	{1, 3, 5, 3, 7, 5, X, X, X, X, X, X, X, X, X, X},
	{0, 8, 7, 0, 7, 1, 1, 7, 5, X, X, X, X, X, X, X},
	{9, 0, 3, 9, 3, 5, 5, 3, 7, X, X, X, X, X, X, X},
	{9, 8, 7, 5, 9, 7, X, X, X, X, X, X, X, X, X, X},
	{5, 8, 4, 5, 10, 8, 10, 11, 8, X, X, X, X, X, X, X},
	{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, X, X, X, X},
	{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, X, X, X, X},
	{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, X},
	{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, X, X, X, X},
	{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, X},
	{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, X},
	{9, 4, 5, 2, 11, 3, X, X, X, X, X, X, X, X, X, X},
	{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, X, X, X, X},
	{5, 10, 2, 5, 2, 4, 4, 2, 0, X, X, X, X, X, X, X},
	{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, X},
	{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, X, X, X, X},
	{8, 4, 5, 8, 5, 3, 3, 5, 1, X, X, X, X, X, X, X},
	{0, 4, 5, 1, 0, 5, X, X, X, X, X, X, X, X, X, X},
	{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, X, X, X, X},
	{9, 4, 5, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{4, 11, 7, 4, 9, 11, 9, 10, 11, X, X, X, X, X, X, X},
	{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, X, X, X, X},
	{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, X, X, X, X},
	{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, X},
	{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, X, X, X, X},
	{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, X},
	{11, 7, 4, 11, 4, 2, 2, 4, 0, X, X, X, X, X, X, X},
	{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, X, X, X, X},
	{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, X, X, X, X},
	{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, X},
	{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, X},
	{1, 10, 2, 8, 7, 4, X, X, X, X, X, X, X, X, X, X},
	{4, 9, 1, 4, 1, 7, 7, 1, 3, X, X, X, X, X, X, X},
	{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, X, X, X, X},
	{4, 0, 3, 7, 4, 3, X, X, X, X, X, X, X, X, X, X},
	{4, 8, 7, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{9, 10, 8, 10, 11, 8, X, X, X, X, X, X, X, X, X, X},
	{3, 0, 9, 3, 9, 11, 11, 9, 10, X, X, X, X, X, X, X},
	{0, 1, 10, 0, 10, 8, 8, 10, 11, X, X, X, X, X, X, X},
	{3, 1, 10, 11, 3, 10, X, X, X, X, X, X, X, X, X, X},
	{1, 2, 11, 1, 11, 9, 9, 11, 8, X, X, X, X, X, X, X},
	{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, X, X, X, X},
	{0, 2, 11, 8, 0, 11, X, X, X, X, X, X, X, X, X, X},
	{3, 2, 11, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{2, 3, 8, 2, 8, 10, 10, 8, 9, X, X, X, X, X, X, X},
	{9, 10, 2, 0, 9, 2, X, X, X, X, X, X, X, X, X, X},
	{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, X, X, X, X},
	{1, 10, 2, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{1, 3, 8, 9, 1, 8, X, X, X, X, X, X, X, X, X, X},
	{0, 9, 1, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{0, 3, 8, X, X, X, X, X, X, X, X, X, X, X, X, X},
	{X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X}
};
#endif
	
#undef XYZ_DIR_EDGE

#undef X

// number of vertices for each case above
uint numVertsTable[256] = {
    0,    3,    3,    6,    3,    6,    6,    9,    
	3,    6,    6,    9,    6,    9,    9,    6,
    3,    6,    6,    9,    6,    9,    9,    12,
    6,    9,    9,    12,    9,    12,    12,    9,
    3,    6,    6,    9,    6,    9,    9,    12,
    6,    9,    9,    12,    9,    12,    12,    9,
    6,    9,    9,    6,    9,    12,    12,    9,
    9,    12,    12,    9,    12,    15,    15,    6,
	3,    6,    6,    9,    6,    9,    9,    12,
    6,    9,    9,    12,    9,    12,    12,    9,
    6,    9,    9,    12,    9,    12,    12,    15,
    9,    12,    12,    15,    12,    15,    15,    12,
    6,    9,    9,    12,    9,    12,    6,    9,
    9,    12,    12,    15,    12,    15,    9,    6,
    9,    12,    12,    9,    12,    15,    9,    6,
    12,    15,    15,    12,    15,    6,    12,    3,
    3,    6,    6,    9,    6,    9,    9,    12,
    6,    9,    9,    12,    9,    12,    12,    9,
    6,    9,    9,    12,    9,    12,    12,    15,
    9,    6,    12,    9,    12,    9,    15,    6,
    6,    9,    9,    12,    9,    12,    12,    15,
    9,    12,    12,    15,    12,    15,    15,    12,
    9,    12,    12,    9,    12,    15,    15,    12,
    12,    9,    15,    6,    15,    12,    6,    3,
    6,    9,    9,    12,    9,    12,    12,    15,
    9,    12,    12,    15,    6,    9,    9,    6,
    9,    12,    12,    15,    12,    15,    15,    6,
    12,    9,    15,    12,    9,    6,    12,    3,
    9,    12,    12,    15,    12,    15,    9,    12,
    12,    15,    15,    6,    9,    12,    6,    3,
    6,    9,    9,    6,    9,    12,    6,    3,
    9,    6,    12,    3,    6,    3,    3,    0,
};

// number of facts for each case above
uint numFactsTable[256] = {
	0,	1,	1,	2,	1,	2,	2,	3,
	1,	2,	2,	3,	2,	3,	3,	2,
	1,	2,	2,	3,	2,	3,	3,	4,
	2,	3,	3,	4,	3,	4,	4,	3,
	1,	2,	2,	3,	2,	3,	3,	4,
	2,	3,	3,	4,	3,	4,	4,	3,
	2,	3,	3,	2,	3,	4,	4,	3,
	3,	4,	4,	3,	4,	5,	5,	2,
	1,	2,	2,	3,	2,	3,	3,	4,
	2,	3,	3,	4,	3,	4,	4,	3,
	2,	3,	3,	4,	3,	4,	4,	5,
	3,	4,	4,	5,	4,	5,	5,	4,
	2,	3,	3,	4,	3,	4,	2,	3,
	3,	4,	4,	5,	4,	5,	3,	2,
	3,	4,	4,	3,	4,	5,	3,	2,
	4,	5,	5,	4,	5,	2,	4,	1,
	1,	2,	2,	3,	2,	3,	3,	4,
	2,	3,	3,	4,	3,	4,	4,	3,
	2,	3,	3,	4,	3,	4,	4,	5,
	3,	2,	4,	3,	4,	3,	5,	2,
	2,	3,	3,	4,	3,	4,	4,	5,
	3,	4,	4,	5,	4,	5,	5,	4,
	3,	4,	4,	3,	4,	5,	5,	4,
	4,	3,	5,	2,	5,	4,	2,	1,
	2,	3,	3,	4,	3,	4,	4,	5,
	3,	4,	4,	5,	2,	3,	3,	2,
	3,	4,	4,	5,	4,	5,	5,	2,
	4,	3,	5,	4,	3,	2,	4,	1,
	3,	4,	4,	5,	4,	5,	3,	4,
	4,	5,	5,	2,	3,	4,	2,	1,
	2,	3,	3,	2,	3,	4,	2,	1,
	3,	2,	4,	1,	2,	1,	1,	0
};